CONSTRAINING SUB-PARSEC BINARY SUPERMASSIVE BLACK HOLES IN QUASARS WITH MULTI-EPOCH SPECTROSCOPY. II. THE POPULATION WITH KINEMATICALLY OFFSET BROAD BALMER EMISSION LINES

A small fraction of quasars have long been known to show bulk velocity offsets (of a few hundred to thousands of km s(-1)) in the broad Balmer lines with respect to the systemic redshift of the host galaxy. Models to explain these offsets usually invoke broad-line region gas kinematics/asymmetry around single black holes (BHs), orbital motion of massive (similar to sub-parsec (sub-pc)) binary black holes (BBHs), or recoil BHs, but single-epoch spectra are unable to distinguish between these scenarios. The line-of-sight (LOS) radial velocity (RV) shifts from long-term spectroscopic monitoring can be used to test the BBH hypothesis. We have selected a sample of 399 quasars with kinematically offset broad H beta lines from the Sloan Digital Sky Survey (SDSS) Seventh Data Release quasar catalog, and have conducted second-epoch optical spectroscopy for 50 of them. Combined with the existing SDSS spectra, the new observations enable us to constrain the LOS RV shifts of broad H beta lines with a rest-frame baseline of a few years to nearly a decade. While previous work focused on objects with extreme velocity offset (> 10(3) km s(-1)), we explore the parameter space with smaller (a few hundred km s(-1)) yet significant offsets (99.7% confidence). Using cross-correlation analysis, we detect significant (99% confidence) radial accelerations in the broad H beta lines in 24 of the 50 objects, of similar to 10-200 km s(-1) yr(-1) with a median measurement uncertainty of similar to 10 km s(-1) yr(-1), implying a high fraction of variability of the broad-line velocity on multi-year timescales. We suggest that 9 of the 24 detections are sub-pc BBH candidates, which show consistent velocity shifts independently measured from a second broad line (either H alpha or Mg II) without significant changes in the broad-line profiles. Combining the results on the general quasar population studied in Paper I, we find a tentative anti-correlation between the velocity offset in the first-epoch spectrum and the average acceleration between two epochs, which could be explained by orbital phase modulation when the time separation between two epochs is a non-negligible fraction of the orbital period of the motion causing the line displacement. We discuss the implications of our results for the identification of sub-pc BBH candidates in offset-line quasars and for the constraints on their frequency and orbital parameters.